U.S. Senate Banking, Housing, and Urban Affairs Committee Chairman Richard Shelby (R., Ala.) said Tuesday his panel will review the Federal Reserve’s structure, given its broad new powers over the financial system.

The 2010 Dodd-Frank law expanded Fed oversight of big banks and tasked it with monitoring financial stability. But Congress didn’t examine whether the Fed was “correctly structured" to account for its new authority, Mr. Shelby said.

“As part of this effort, we will review proposals aimed at providing greater clarity in Fed decision-making and at reforming the composition of Federal Reserve System,” he said at the committee’s first hearing on Fed “reforms” since Republicans took control of the upper chamber in January. Mr. Shelby said he had asked for input from the Fed’s regional reserve bank presidents.

Sen. Sherrod Brown (D., Ohio), the committee’s top Democrat, also said Congress should consider whether the current governance of the Fed system “appropriately holds regulators accountable and encourages diverse perspectives.”

The Fed system comprises a seven-member Washington-based board of governors and 12 regional reserve banks run by their own presidents. The governors are nominated by the U.S. president and are subject to Senate confirmation. The reserve bank presidents are chosen by the banks’ board of directors, subject to approval by the board of governors.

“With independent and accountable leaders, diverse perspectives, and strong regulation, the Federal Reserve System can be responsive to the American public,” Mr. Brown said. “This is where we should focus our discussion of reforms of the Federal Reserve System.”

“Some changes would require legislation, but some would not,” he added.

The comments come as several proposals for restructuring the Fed are gaining attention on Capitol Hill.

Sen. Jack Reed (D., R.I.) reintroduced a measure last month that would require the president to nominate and the Senate to confirm the president of the Federal Reserve Bank of New York. Mr. Reed unveiled the bill late last year amid criticism that the New York Fed wasn’t doing a good enough job policing Wall Street. The lawmaker argued that the unique and powerful position required greater scrutiny from Congress and the public.

Federal Reserve Bank of Dallas President Richard Fisher has proposed shifting power away from the New York Fed to other regional banks. He also suggested changing the current rotation pattern of the bank presidents as voting members of the Fed’s policy making Federal Open Market Committee.

Mr. Fisher’s plan earned an important endorsement from the Independent Community Bankers of America, which called on the Senate to adopt the changes.

The Fed did not immediately comment on Mr. Shelby’s remarks. But Fed Chairwoman Janet Yellen did say at a Senate Banking Committee hearing last week that the Fed’s structure “is a matter for Congress to decide.” She added, “I think the current structure works well, so I wouldn't recommend changes.”